   # Graphing Calculator Activities Graph f ( x ) = | x | , f ( x ) = 2 | x | , f ( x ) = 4 | x | , and f ( x ) = 1 2 | x | on the same set of axes. Graph f ( x ) = | x | , f ( x ) = − | x | , f ( x ) = − 3 | x | , and f ( x ) = − 1 2 | x | on the same set of axes. Use your results from parts (a) and (b) to make a conjecture about the graphs of f ( x ) = a | x | , where a is a nonzero real number. Graph f ( x ) = | x | , f ( x ) = | x | + 3 , f ( x ) = | x | − 4 , and f ( x ) = | x | + 1 on the same set of axes. Make a conjecture about the graphs of f ( x ) = | x | + k , where k is a nonzero real number. Graph f ( x ) = | x | , f ( x ) = | x − 3 | , f ( x ) = | x − 1 | , and f ( x ) = | x + 4 | on the same set of axes. Make a conjecture about the graphs of f ( x ) = | x − h | , where h is a nonzero real number. On the basis of your results from parts (a) through (e), sketch each of the following graphs. Then use a graphing calculator to check your sketches. f ( x ) = | x − 2 | + 3 f ( x ) = | x + 1 | − 4 f ( x ) = 2 | x − 4 | − 1 f ( x ) = − 3 | x + 2 | + 4 f ( x ) = 1 2 | x − 3 | − 2 ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728

#### Solutions

Chapter
Section ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728
Chapter 9.2, Problem 61PS
Textbook Problem
1 views

## Graphing Calculator Activities Graph f ( x ) = | x | , f ( x ) = 2 | x | , f ( x ) = 4 | x | , and f ( x ) = 1 2 | x | on the same set of axes. Graph f ( x ) = | x | , f ( x ) = − | x | , f ( x ) = − 3 | x | , and f ( x ) = − 1 2 | x | on the same set of axes. Use your results from parts (a) and (b) to make a conjecture about the graphs of f ( x ) = a | x | , where a is a nonzero real number. Graph f ( x ) = | x | , f ( x ) = | x | + 3 , f ( x ) = | x | − 4 , and f ( x ) = | x | + 1 on the same set of axes. Make a conjecture about the graphs of f ( x ) = | x | + k , where k is a nonzero real number. Graph f ( x ) = | x | , f ( x ) = | x − 3 | , f ( x ) = | x − 1 | , and f ( x ) = | x + 4 | on the same set of axes. Make a conjecture about the graphs of f ( x ) = | x − h | , where h is a nonzero real number. On the basis of your results from parts (a) through (e), sketch each of the following graphs. Then use a graphing calculator to check your sketches. f ( x ) = | x − 2 | + 3 f ( x ) = | x + 1 | − 4 f ( x ) = 2 | x − 4 | − 1 f ( x ) = − 3 | x + 2 | + 4 f ( x ) = 1 2 | x − 3 | − 2

To determine

(a)

To graph:

The functions f(x)=|x|, f(x)=2|x|, f(x)=4|x|, and f(x)=12|x| on the same set of axes.

### Explanation of Solution

Approach:

Use a graphing utility to graph the given functions.

• Press Y= to enter the equations.
• Press MATH go to NUM menu and select absolute function.
• Press GRAPH button to display the final graph.

Calculation:

Use a graphing utility to graph the functions f(x)=|x|, f(x)=2|x|, f(x)=4|x|, and f(x)=12|x| on the same set of axes.

Press Y= to enter the equations

To determine

(b)

To graph:

The functions f(x)=|x|, f(x)=|x|, f(x)=3|x|, and f(x)=12|x| on the same set of axes.

To determine

(c)

To conjecture:

The graphs of f(x)=a|x|, here a is a nonzero real number from the results of parts (a) and (b).

To determine

(d)

To graph:

The functions f(x)=|x|, f(x)=|x|+3, f(x)=|x|4, and f(x)=|x|+1 on the same set of axes and to make a conjecture about the graphs of f(x)=|x|+k, here k is a nonzero real number.

To determine

(e)

To graph:

The functions f(x)=|x|, f(x)=|x3|, f(x)=|x1|, and f(x)=|x+4| on the same set of axes and to make a conjecture about the graphs of f(x)=|xh|, here h is a nonzero real number.

To determine

(f)

To sketch:

The graphs of the given functions and use a graphing calculator to check these sketches.

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